Chapter 9
Resource Allocation
Chapter 9 Resource Allocation
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Introduction
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This chapter addresses:
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Trade-offs involved to crash cost
Relationship between resource loading and
leveling
Some approaches used to solve allocation
problem
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Critical Path Method – Crashing a Project
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One important difference between CPM & PERT:
 CPM included a way of relating the project
schedule to the level of physical resources
trade time for cost, or vice versa
Can specify 2 activity times and 2 costs
1st time/cost combination- called normal
2nd combination called crash
Normal – usual ‘average’ time, resources
Crash – expedite by applying additional resources
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Critical Path Method – Crashing a Project
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Allocation problem requires more careful
consideration-additional resources?
Many things make crashing a way of life on
some projects (i.e last minutes changes in
client specification, without permission to
extend the project deadline by an appropriate
increment)
Careful planning is critical when crashing
project – need to consider feasibility of
expediting work (e.g equipment availability)
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Critical Path Method – Crashing a Project
Slope = crash cost – normal cost
crash time – normal time
Where: slope = cost per day of crashing a
project
When slope is negative : indicate the time
required for a project is decreased, the cost
is increased
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The dollars per day slope of activities is
relevant only if the whole crash increment is
useful
Crashing may involve a relatively simple
decision to increase groups of resources
(labor-shovel, Ditch-Witch Technology)
If do changes in technology tend to produce
discontinuities in outcomes and also in cost.
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Principles to crash a project
1.
1.
Focus on the critical path when trying to
shorten the duration [resource ready]
Select the least expensive way to do it
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Crashing a Project (E.g Two-Time CPM)
Activity
Precedenc
e
Duration,
Cost, $
Days
(normal,crash)
(normal,crash)
a
-
3,2
40, 80
40/-1 = -40
b
a
2,1
20, 80
60/-1 = -60
c
a
2,2
20, 20
Cannot be
expedited
d*
a
4,1
30, 120
90/-3 = -30
e**
b
3,1
10, 80
-70 (2 days)
*Partial crashing allowed
**Partial crashing not allowedChapter 9 Resource Allocation
Slope ($/day)
8
A CPM Example
e
b
a
c
d
1
2
3
4
5
6
7
8
Normal Schedule, 8 days, $120
Chapter 9 Resource Allocation
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e
b
a
e
b
a
c
c
d
1
2
3
d
4
5
6
7
8
1
7-day schedule, $160
2
3
6
7
8
e
b
b
a
c
c
d
d
1
5
6-day schedule. $220
e
a
4
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
4-day schedule, $350
5-day schedule, $260
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Network critical path is a-b-e, project duration
is 8 days, normal total cost is $120
The decision about which activities to crash
depends on how much to reduce the duration
On the benefit side, some projects have
penalty clauses that make the parent
organization liable for late deliverysometimes bonuses for early delivery
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On the cost side, figure below shows the time/cost
relationship of crashing the project
Cost ($)

400
350
300
250
200
150
100
50
0
All crash
a + b + 2d + 2e
a + d + 2e - b
a+b
a
All normal
0
1
2
3
4
5
6
7
8
9
Total duration (days)
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Fast Tracking
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Another way to expedite a project
Term used for construction projects
Refers to overlapping design and build phases
Design completed before construction
starts,so overlapping will result shortening
the project duration
Build before design completed-more design
changes
Loss productivity, increased cost, loss time
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Fast Tracking (cont.)
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Studies revealed that:
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more design changes in fast tracking – the
number of project change orders not significantly
different than not fast-tracked project
Dependent on effective feed-back and feedforward communication
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SOLVED PROBLEM
2
c
4
b
e
3
Crash
Time,
Cost
Normal Partial
Time, crashing
Cost
a
3,$60
3,$60 No
b
6,80
7,30
Yes
c
2,90
5,50
No
d
5,50
6,30
No
e
2,100
4,40
Yes
d
a
1
Activity
Find the lowest cost to complete the project in 10 days
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Answer
Current time and cost: 12 days and $210
Since the critical path is a-c-e, we only
initially need consider these 3 activities:
3
2
0
3
a
d
c
1
a: cannot be crashed
6
5
7
b
4
4
3
8
12
e
c: can cut 3 days at an extra cost of $40
but only results in project completion by
day 11, due to b. To reach 10 days, cut
b by 1 day, total extra cost $90
e: can cut e by 2 days for an extra cost of
$60 and results in project completion by
day 10.
Thus, cut e 2 days at a cost of $60.
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RESOURCE ALLOCATION PROBLEM
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A fundamental measure of the PM’s success
in project mgmt is the skill with which the
trade-offs among performance, time and cost
are managed
The extreme points of the relationship
between time use and resource are:
 Time limited
 Resource limited
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RESOURCE LOADING
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The amount of individuals resources an existing
schedule requires during specific time periods
Resource loading can be illustrated by:
 Resource usage calendar
 Modified PERT/CPM AOA diagram (similar with
Gantt Chart)
PM responsibility:
 Demand for resources does not exceed resource
capacities
 Ensure that the required resources, in the required
amounts
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Resource Usage Calendar
Chapter 9 Resource Allocation
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Modified PERT/CPM AOA Diagram
(Refer Ch 08 Slide 26)
a
1
d
2
(4,0)
6
(0,2)
(2,1)
3
1
1
c
3
(2,1)
4
(3,1)
4
0
5
10
(0,6)
g
f
(1,1)
i
5
(6,3)
(1,0)
dummy
7
e
3
b
j
h
(0,2)
15
20
25
Chapter 9 Resource Allocation
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35
40
45
20
RESOURCE LEVELING
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Aims to minimize the period-by-period variations in
resource loading by shifting tasks within their slack
allowances
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Purpose to create a smoother distribution of resource
usage
Advantages;
 Much less hands on management
 Be able to use ‘just in time’ inventory policy with
right quantity delivered
If the resource being leveled is people, it improves
morale and results in fewer problems in the
personnel and payroll offices
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E.g: Network
2
a, 2
[2]
1
b, 3
[2]
c, 5
[4]
4
3
The activity time is shown above the arc, and resource usage
(one resource, workers) Chapter
is in9 Resource
brackets
below the arc.
Allocation
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Before Resource Leveling
a
a
b
c
c
c
b
1
2
3
Days
4
5
Chapter 9 Resource Allocation
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c
b
2
Days
3
4
5
23
After Resource Leveling
a
b
a
b
c
c
1
2
3
Days
4
5
Chapter 9 Resource Allocation
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2
3
Days
4
5
24
RESOURCE LOADING/LEVELING AND
UNCERTAINTY
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If happens excess capacity,the alternative
that we can consider:


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Try to level the demand, moving some of it
forward and some backward
Try to alter the supply of working hours-trade off
time between periods of over capacity and periods
of under capacity
Might expend additional resources-contract worker
for overload period, subcontract the workload

Which cheaper?Delay or subcontract?
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